Review for Test DIA Summative

Word Problems What are you trying to find Assign a variable Tell what the variable stands for Reread problem and write equation in terms of the variable Solve the equation Make sure you are answering the problem

Example Kevin is buying a motorcycle from his friend Bruce for $2,950. If he gives him a deposit of $500 and agrees to pay $175 each month until it is paid off, write an equation to determine how long it will take to pay off the motorcycle.

Example One tree is 4 feet less than twice the height of another tree. The sum of their heights is 284 feet. What is the height of the taller tree?

Literal Equations Literal equations are equations which contain more than one variable. We can manipulate them to “highlight” (solve for another term) by using our properties of equality and the distributive property to isolate the new variable we want to solve for onto one side of the equation. Remember you cannot combine terms that are different (x’s with y’s, numbers with letters, etc.), so just write them next to each other Your answer will not be a number, it will be a “complicated” algebraic expression

Example d + 3n = 1 (solve for n) bc + 3g = 2k (solve for c)

Word problems with sales tax If the sales tax in Florida is 7%, how can you write an equation to find the cost of buying a number of items that cost $12 each?

Solutions of an equation represented by a graph If you are given a graph of an equation and asked to state the solutions of the equation, remember that each point on the graph represents a pair of coordinates (x,y) that make the equation true So to give the solutions, simply find the points on the graph that the line intersects and identify the coordinates of those points

Word problems as functions If this sequence of numbers shows the number of miles Gabriella has ridden her bike after each of the first four weeks of training, and the pattern of her miles ridden remains the same, which function could be used to determine the number of miles she had ridden at the end of week x? 5, 9, 13, 17,… f(x) = 5x f(x) = 5x - 1 f(x) = x + 5 f(x) = 4x + 1

Domain and range of a function From a table (domain is all x values and range is all y values) From a set of ordered pairs: (-3, -2), (0, 5), (4, 7) Domain is (-3, 0, 4); Range is (-2, 5, 7) From a graph (domain is the x coordinates of the points and range is the y coordinates of the points) From a mapping diagram (domain includes the inputs or x values and range includes the outputs or y values)

Rate of change The formula to find the average rate of change is:

Slope-intercept form The slope-intercept form of an equation is: y = mx + b m is the slope of the line b is the y-intercept (what does changing b do?)

Arithmetic sequences There is a constant difference between successive terms of an arithmetic sequence (you will see a pattern) To continue a sequence, find that pattern and continue it for as many terms as you need Find the tenth term of the following sequences: 3, 7, 11, 15, … 16, 7, -2, -11, …